In a semiconductor manufacturing process, transistors in an LSI are often formed by utilizing a line and space structure. FIG. 30 is a plan view showing an example of a semiconductor substrate 900. The semiconductor substrate 900 has a line and space structure composed of line portions 910 and space portions 920; transistor structures such as gate electrodes are fabricated into such a line and space structure. A gate length is an important parameter for determining the properties of a transistor, and the suppression of variations thereof to a predetermined value or less is a very important factor for determining the performance of an LSI. The minimum length in such an element structure is referred to as a CD (critical dimension). If transistors having significantly different properties such as a threshold voltage and a gate current are installed within a circuit, it is impossible to assure the performance of an LSI that is an aggregation thereof. In order to prevent the foregoing problem, it is necessary to constantly optimize semiconductor manufacturing process conditions.
Even in other processes, factors for changing the CD value of similar elements are constantly present. Therefore, in a wafer that is being actually manufactured, is it a very important issue to check the CD value at the right time. Conventionally, in the measurement of the CD of a semiconductor and the like, a CD-SEM or a light scattering analysis method (scatterometry) is used.
In contrast, there is proposed a technology for analyzing density fluctuation in a nonuniform density multilayer film where one or more nonuniform density films are stacked on a substrate through the use of a scattering function representing an X-ray scattering curve according to a parameter indicating the distribution state of particlelike material (for example, patent document 1).
In the nonuniform density multilayer film analyzing method disclosed in patent document 1, the scattering function representing the X-ray scattering curve according to the parameter indicating the distribution state of particlelike material is used. An X-ray scattering intensity is calculated under the same conditions as measurement conditions under which the X-ray scattering intensity is actually measured, fitting is performed between the X-ray scattering intensity calculated while a parameter is being changed and the actually measured X-ray scattering intensity, and the value of the parameter when the calculated X-ray scattering intensity agrees with the actually measured X-ray scattering intensity is set as the distribution state of particlelike material within the nonuniform density multilayer film. As described above, as the scattering function, through the use of a function introducing a transition probability, in which an exact solution of the multilayer film without scattering in an interface is set as an initial state and a final state, the distribution state of particlelike material within the nonuniform density multilayer film is analyzed.
In a method disclosed in patent document 2, in order to measure the critical dimension (CD), the surface of a substrate is irradiated with an X-ray beam so as to hit a region of a periodic structure on the surface of a specimen. Then, in order to measure the dimension of the structure parallel to the surface of the specimen, an X-ray pattern resulting from scattering corresponding to the feature of the surface is detected as the function of an azmuth parallel to the surface of the specimen. However, as the method of measuring the diffraction line of each order of the formed periodical structure, the rotation of the specimen itself in the direction of the azmuth is not explicitly indicated.
In contrast, non-patent document 1 disclosed before the disclosure of patent document 2 described above discloses that a high resolution measurement system is configured through the use of a mirror, a crystal collimator and an analyzer, a diffracted X-lay from a periodical structure formed on the surface is referred to as an in-plane X-ray small angle scattering pattern and is measured as the function of an azmuth. In the method disclosed here, the periodical structure is regarded as almost like crystal, a specimen is rotated in the direction of the azmuth such that the spectrum of each diffraction order satisfies the well-known Bragg diffraction conditions (in non-patent document 1, it is represented as φ), an extremely large number of diffraction peaks are detected, and based on it, the pitch and the line width of the periodical structure are determined with a high degree of accuracy. Furthermore, a method is disclosed in which, at the same time when the specimen is rotated in the direction of the azmuth, a detector is rotated at a speed twice as high as such a speed (in non-patent document 1, it is represented as 2θ/φ scan), and thus the Bragg diffraction conditions are satisfied.
Furthermore, non-patent document 2 proposes a structure model for theoretically calculating a scattered X-ray spectrum that is a function with reference to the direction of the measured azmuth (formula (2) in non-patent document 2). A method is disclosed in which, based on this, a scattered X-ray intensity is specifically calculated, a parameter is optimized by comparison with the measured scattered X-ray spectrum, a microstructure such as a line width and the inclination of a side wall is determined.    Patent document 1: Japanese Unexamined Patent Application Publication No. 2003-202305    Patent document 2: US patent Application Publication No. 2006/133570    Non-Patent document 1: Yoshiyasu ITO, Katsuhiko INABA, Kazuhiko OMOTE, Yasuo WADA, Tomokazu EZURA, Ken TSUTSUI, and Susumu IKEDA, “Evaluation of a Microfabricated Structure by an Ultra-high Resolution In-plane X-ray Small Angle Scattering Method,” The 53th Applied Physics Related Discussion Meeting Preprint 24a-B-4/III, May 24, 2006, No. 3, p. 1471    Non-Patent document 2: Yoshiyasu ITO, Katsuhiko INABA, Kazuhiko OMOTE, Yasuo WADA, and Susumu IKEDA, Characterization of Submicron-scale Periodic Grooves by Grazing Incidence Ultra-small-angle X-ray Scattering, Japanese Journal of Applied Physics, Japan, The Japan Society of Applied Physics, Aug. 10, 2007, Vol. 46, No. 32, 2007, pp. L773-L775